Intertwining Defects and Fermion-Boundary Scattering from TQFT

Abstract

We construct conformal boundary conditions of free Dirac fermions that preserve chiral, anomaly-free symmetries, and determine the associated fermion-boundary scattering, using the TQFT/CFT framework. We apply the construction to several previously unresolved examples: higher-charge monopoles in non-chiral QED, a family of $SU(N)\times SU(N+2)$-symmetric models, the chiral QED with charges $\{1^5,3,(-2)^4\}$, and the charge-three monopole of the Standard Model. In these examples, out-going states are created by defect operators at the end of non-invertible topological lines; when such a line is non-simple, the out-going state splits into superselection sectors, and we give a formula for the branching ratios in terms of TQFT data. We also propose a general construction that adds and then gaps neutral spectators, under a technical assumption, which is potentially applicable to the 1-5-7-8-9 model.